Saturday, 10 March 2018

A group of people with assorted eye colors (say 10 blue and 10 brown) live on an island.

No one knows the color of their eyes as there are no mirrors on the island and the water is muddy so you can't use the reflection. For all each person knows, they could have green eyes!

However, everyone can see the eye colour of everyone else, but they can't communicate to each other to tell each other their eye colour.

Every night
at midnight, a ferry stops at the island. Any islanders who have
figured out the color of their own eyes can leave the island.

One day a sailor from the ferry gets off the boat and says:

"I can see someone who has blue eyes".

Everyone hears and understand the statement, but the sailor is immediately shot dead for communicating with the islanders and no-one ever speaks again. However, given this information some people are able to figure out their eye colour.

Wednesday, 7 March 2018

Suppose
you are going to play chess against two people: one person is really
good, one person is quite bad. You are going to play three games and you
always have to alternate your opponents. Namely, you can either choose
to play the opponents in the order

Good, Bad, Good,

or you can play the opponents in the order

Bad, Good, Bad.

Which of these two play sequences gives you the optimal chance of winning two consecutive games?

You can approach this problem using probability and tree diagrams. However a little logic goes a long way.

Specifically, in order to win two consecutive games you have to win the middle game. Thus, it is best to put your weaker opponent in the middle. Thus, Good, Bad, Good is the best strategy.

An alternative way of also seeing this answer it that you're probably going to lose against the good player, so the Good, Bad, Good play order gives you two chances to win against the good player, rather than just one.

Simple no?

If you want a bit more rigor then Ben has created a YouTube video solution.

Alternatively, you could try three player chess and team up with the
weak player to beat the good player. But that might be considered
cheating...

Friday, 2 March 2018

Suppose you are going to play chess against two people: one person is really good, one person is quite bad. You are going to play three games and you always have to alternate your opponents. Namely, you can either choose to play the opponents in the order

Good, Bad, Good,

or you can play the opponents in the order

Bad, Good, Bad.

Which of these two play sequences gives you the optimal chance of winning two consecutive games?